# Teaching According to Students' Aptitude: Personalized Mathematics Tutoring via Persona-, Memory-, and Forgetting-Aware LLMs

arXiv: https://arxiv.org/abs/2511.15163 · HTML: https://mlsanity.com/paper/2511.15163/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 67 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [ChemCrow: Augmenting large-language models with chemistry tools](https://mlsanity.com/paper/2304.05376/) (2023)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [Context-Aware Attentive Knowledge Tracing](https://mlsanity.com/paper/2007.12324/) (2020)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Llama2Vec: Unsupervised Adaptation of Large Language Models for Dense Retrieval](https://mlsanity.com/paper/2312.15503/) (2023)
- [Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge](https://mlsanity.com/paper/2007.12061/) (2020)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Exploring Knowledge Tracing in Tutor-Student Dialogues using LLMs](https://mlsanity.com/paper/2409.16490/) (2024)
- [EduAgent: Generative Student Agents in Learning](https://mlsanity.com/paper/2404.07963/) (2024)
- [MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems](https://mlsanity.com/paper/2404.04735/) (2024)
- [Empowering Personalized Learning through a Conversation-based Tutoring System with Student Modeling](https://mlsanity.com/paper/2403.14071/) (2024)
- [MathAgent: Leveraging a Mixture-of-Math-Agent Framework for Real-World Multimodal Mathematical Error Detection](https://mlsanity.com/paper/2503.18132/) (2025)
- [Training Turn-by-Turn Verifiers for Dialogue Tutoring Agents: The Curious Case of LLMs as Your Coding Tutors](https://mlsanity.com/paper/2502.13311/) (2025)
- [One Size doesn't Fit All: A Personalized Conversational Tutoring Agent for Mathematics Instruction](https://mlsanity.com/paper/2502.12633/) (2025)
- [Math Agents: Computational Infrastructure, Mathematical Embedding, and Genomics](https://mlsanity.com/paper/2307.02502/) (2023)
- [Using Generative AI and Multi-Agents to Provide Automatic Feedback](https://mlsanity.com/paper/2411.07407/) (2024)
- [The Effects of Embodiment and Personality Expression on Learning in LLM-based Educational Agents](https://mlsanity.com/paper/2407.10993/) (2024)
- [Elevating Legal LLM Responses: Harnessing Trainable Logical Structures and Semantic Knowledge with Legal Reasoning](https://mlsanity.com/paper/2502.07912/) (2025)
- [Knowledge-Infused Legal Wisdom: Navigating LLM Consultation through the Lens of Diagnostics and Positive-Unlabeled Reinforcement Learning](https://mlsanity.com/paper/2406.03600/) (2024)
- [ROSE: A Reward-Oriented Data Selection Framework for LLM Task-Specific Instruction Tuning](https://mlsanity.com/paper/2412.00631/) (2024)
- [FOKE: A Personalized and Explainable Education Framework Integrating Foundation Models, Knowledge Graphs, and Prompt Engineering](https://mlsanity.com/paper/2405.03734/) (2024)
- [AI-Powered Math Tutoring: Platform for Personalized and Adaptive Education](https://mlsanity.com/paper/2507.12484/) (2025)
- [Community-Based Hierarchical Positive-Unlabeled (PU) Model Fusion for Chronic Disease Prediction](https://mlsanity.com/paper/2309.03386/) (2023)
- [AI-VERDE: A Gateway for Egalitarian Access to Large Language Model-Based Resources For Educational Institutions](https://mlsanity.com/paper/2502.09651/) (2025)
- [LearnMate: Enhancing Online Education with LLM-Powered Personalized Learning Plans and Support](https://mlsanity.com/paper/2503.13340/) (2025)

## Built on by (most cited first, 3 of 3)

- ["Excuse me, may I say something..." CoLabScience, A Proactive AI Assistant for Biomedical Discovery and LLM-Expert Collaborations](https://mlsanity.com/paper/2604.15588/) (2026)
- [CamPilot: A Multi-Agent Cinematic Assistant for Camera-Controlled Movie Generation](https://mlsanity.com/paper/2609.10943/) (2026)
- [RegulaTutor: A Theory-Informed Framework for Long-Term Personalized Learning](https://mlsanity.com/paper/2610.13399/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly integrated into intelligent tutoring systems to provide human-like and adaptive instruction. However, most existing approaches fail to capture how students' knowledge evolves dynamically across their proficiencies, conceptual gaps, and forgetting patterns. This challenge is particularly acute in mathematics tutoring, where effective instruction requires fine-grained scaffolding precisely calibrated to each student's mastery level and cognitive retention. To address this issue, we propose TASA (Teaching According to Students' Aptitude), a student-aware tutoring framework that integrates persona, memory, and forgetting dynamics for personalized mathematics learning. Specifically, TASA maintains a structured student persona capturing proficiency profiles and an event memory recording prior learning interactions. By incorporating a continuous forgetting curve with knowledge tracing, TASA dynamically updates each student's mastery state and generates contextually appropriate, difficulty-calibrated questions and explanations. Empirical results demonstrate that TASA achieves superior learning outcomes and more adaptive tutoring behavior compared to representative baselines, underscoring the importance of modeling temporal forgetting and learner profiles in LLM-based tutoring systems.